- 2000 by Peking University Press All rights of reproduction in any form reserved. This paper provides a simple, feasible, and continuous mechanism whose Nash allocations and strong Nash allocations coincide with constrained Walrasian allocations for pure exchange economies. This mechanism allows not only preferences and initial endowments but also coalition patterns to be privately observed, a feature missing from much recent work in implementation theory. Unlike most mechanisms proposed in the literature, our mechanism works not only for three or more agents, but also for two-agent economies, and thus it is a unified mechanism which is irrespective of the number of agents. In addition, our implementation result is obtained without modifying individuals' preferences and thus it improves the mechanism proposed in Peleg (1996) with- out having to define artificial preference relations on price messages announced by individuals.